CGAL users discussion list

[Juan Carlos Lopez Alfonso <>]

Hi 
Sebastien:

About your question: The points of an almost coplanar thetraedra are not in plane with axis aligned normal vectors. In one of my emails, I sent a real example of a resultant thetraedra, where the points of its vertices are almost coplanar when I use the coplanar test of CGAL:

p1x = 0.00000000000000000;

p1y = 0.20000000000000001;

p1z = 0.00000000000000000;

p2x = 0.20000000000000001;

p2y = 0.20000000000000001;

p2z = 0.20000000000000001;

p3x = 0.40000000000000002;

p3y = 0.80000000000000004;

p3z = 1.00000000000000000;

p4x = 0.20000000000000001;

p4y = 0.40000000000000002;

p4z = 0.40000000000000002;

In this example these points are not in plane with axis aligned normal vectors, so How Can I do exactly coplanar this points? (How Daliel says) For this simple example the jacobian is equal to 0, but in CGAL these points are almost coplanar. Therefore, there are thetraedra with the volume very close to 0, where its points are not in a horizontal or vertical plane.

For your answers, I deduce that using any library, will I obtain the same delaunay triangulations for the same distribution of points? (How Monique says)

What happens, if I create two triangulations in CGAL, where the input list of points are in different orders?

Well, anyway thank you very much and best regards 

Juan Carlos

On Mon, Jan 23, 2012 at 9:01 AM, Sebastien Loriot (GeometryFactory) <> wrote:

On 01/23/2012 12:37 AM, Juan Carlos Lopez Alfonso wrote:

Hi There

Again I want to ask about the coplanar test in 3D Delaunay
triangulation, because after read the documentation I have not solved my
problem. I have tested different Delaunay tirangulations and in
different cases (different distributions of points) the resultant
triangulations have several almost coplanar tetrahedras (very very small
volume) and these are no very good triangulations. Before attempting to
use another library to triangulate, I have some questions:

- if Delaunay  triangulations are not uniques, Are there forms in Cgal
to obtian different Delaunay triangulations for the same point
distributions? in order to avoid this problem.

- Are there forms in CGAL to impose a minimum volume for tetrahedras?
something like a epsilon?

Again no.

On the other hand, I still do not understand how in cgal when the
jacobian using double precision is equal to zero, the triangulation give
us coplanar tetrahedras (where the jacobians are about 1.0e-18). I will
use this triangulation to optimizing a variational problem, and when the
algorithm detect this tetrahedras the results are unexpected and erroneous.

Could you give suggestions to obtain better triangulations?

Your points are in plane with axis aligned normal vectors right?
Make your points really coplanar and ALMOST coplanar tetrahedra will
disappear.

Sebastien.

Sorry for these successive questions, but I dont know what I need to do
to solve this problem, which is the only thing I need to complete the
practical part of my model.

Best Regards and thank you in advance
Juan Carlos

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